A multi-disciplinary approach is proposed that will develop new theory, methods, and applications to five significant problems in genetic analysis. The methods include mathematical modeling, statistical formulation, writing appropriate computer programs, development of estimation procedures, Monte Carlo simulation to explore the properties of the estimators, and applications to various sets of actual empirical data. The empirical data will deal with diabetes, high blood pressure, several sets of linkage data, Marfan syndrome, hereditary polyposis coli, Alzheimer and Huntington diseases, reinitis pimentosa, and Usher's syndrome. However, this proposal does not seek funding for the collection of these data. The fields of study involved are genetics, statistics, applied mathematics, epidemiology, clinical medicine and psychiatry. The strategic goals include developing methods of analysis tailored to the authentic details of common clinical diseases (as opposed to omnibus solutions thought suitable for universal application). The specific projects deal respectively with I. Development of models of certain classes of types of homeostatic processes especially adapted to the physiological properties of diabetes and hypertension and their genetic implications. II. Studies on the statistical application of certain models already investigated, to simulated and actual data. III. Exploration of systematic methods of unifying and reconciling data from various sources on the organization of the genome (multipoint linkage analysis, gene assignment, etc.) and a detailed exploration of their statistical properties. IV. A systematic study of the best use of data to estimate the prevalence of a chronic genetic disorder, the data being ascertained in various ways and from multiple lists. V. Analysis of dependence of penetrance (manifestation) of a Mendelian disorder on covariables, notably age, and the connection between the estimation of penetrance and life-table analysis.